Year 7 Edexcel Maths: Core Knowledge Points | Year 7 Edexcel 数学：核心知识点梳理

📚 Year 7 Edexcel Maths: Core Knowledge Points | Year 7 Edexcel 数学：核心知识点梳理

Starting Year 7 Maths can feel like a big jump, but with the Edexcel curriculum, you’ll build a strong foundation in numbers, algebra, geometry and data handling. This article walks you through the key topics you need to know, explained in simple steps with paired English and Chinese explanations.

进入七年级数学可能会感觉像是一个大跨越，但通过Edexcel课程，你将在数字、代数、几何和数据处理方面打下坚实的基础。这篇文章带你梳理必须掌握的核心知识点，用简单明了的步骤和英中对照讲解。

1. Number and Place Value | 数字与位值

Understanding place value helps you read and write large numbers. In Year 7, you work with numbers up to millions and beyond, recognising the value of each digit according to its position (units, tens, hundreds, thousands, etc.). You also learn to round numbers to the nearest 10, 100, or 1000.

理解位值有助于读写大数。在七年级，你要处理高达百万及以上的数字，根据数字的位置（个位、十位、百位、千位等）识别每个数字的值。还要学会将数字四舍五入到最近的10、100或1000。

You also compare and order integers and decimals using inequality symbols: < (less than), > (greater than), and = (equal to). For example, 567 > 432 and 3.45 < 3.54.

你还使用不等号比较和排序整数与小数：<（小于）、>（大于）和 =（等于）。例如，567 > 432、3.45 < 3.54。

Place value extends to decimal fractions, where each column after the decimal point represents tenths, hundredths, thousandths, etc.

位值扩展到小数，小数点后的每一列代表十分位、百分位、千分位等。

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2. Addition and Subtraction of Integers | 整数的加法和减法

You should be confident adding and subtracting whole numbers mentally and using written methods (column addition and subtraction). In Year 7, you apply these skills to solve multi-step word problems and check your answers using inverse operations.

你应该能够自信地心算和用竖式方法（列竖式加法和减法）进行整数的加减运算。在七年级，你要运用这些技能解决多步骤的文字题，并用逆运算检验答案。

Key vocabulary: sum (addition result), difference (subtraction result), addends, minuend, subtrahend. Knowing these terms helps you understand problem instructions.

关键术语：和（加法结果）、差（减法结果）、加数、被减数、减数。了解这些术语有助于理解题目要求。

Estimation is also important: round numbers before calculating to get an approximate answer, then compare with the exact answer.

估算也很重要：先四舍五入再计算得到近似值，然后与精确答案对比。

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3. Multiplication and Division | 乘法和除法

You revise times tables up to 12 × 12 and use formal methods for multiplying and dividing larger numbers, including long multiplication and short division. You also encounter multiplying and dividing by powers of 10, which shifts the decimal point.

你复习到12×12的乘法表，并使用正规方法进行较大数的乘除，包括长乘法和短除法。你还会遇到乘以或除以10的幂，这会使小数点移位。

For example, 3.7 × 100 = 370 (the decimal point moves two places right), and 84 ÷ 1000 = 0.084 (moves three places left).

例如，3.7 × 100 = 370（小数点向右移两位），84 ÷ 1000 = 0.084（向左移三位）。

You solve problems involving factors, multiples, and understanding that division can leave a remainder expressed as a fraction or decimal.

你要解决涉及因数和倍数的问题，并理解除法可能会产生余数，余数可以表示为分数或小数。

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4. Factors, Multiples and Primes | 因数、倍数与质数

A factor is a number that divides exactly into another number without leaving a remainder. For example, factors of 12 are 1, 2, 3, 4, 6, 12. A multiple is the product of a number and an integer; multiples of 7 include 7, 14, 21, 28…

因数是指能整除另一个数而没有余数的数。例如，12的因数是1、2、3、4、6、12。倍数是一个数与整数的乘积；7的倍数有7、14、21、28……

Prime numbers have exactly two distinct factors: 1 and itself. The first few primes are 2, 3, 5, 7, 11, 13. 1 is not prime. Prime factorisation expresses a number as a product of its prime factors; for instance, 60 = 2² × 3 × 5.

质数恰好有两个不同的因数：1和本身。头几个质数是2、3、5、7、11、13。1不是质数。质因数分解是将一个数表示为质因数的乘积；例如，60 = 2² × 3 × 5。

You find the highest common factor (HCF) and lowest common multiple (LCM) using lists or prime factorisation. This is essential for working with fractions.

你用列举法或质因数分解法找出最大公因数（HCF）和最小公倍数（LCM）。这对处理分数至关重要。

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5. Fractions, Decimals and Percentages | 分数、小数与百分比

Year 7 students compare and order fractions, decimals and percentages, and convert between them. Common equivalences like 1/2 = 0.5 = 50% and 1/4 = 0.25 = 25% must be memorised.

七年级学生要比较和排序分数、小数和百分比，并在它们之间转换。像1/2 = 0.5 = 50%、1/4 = 0.25 = 25%这样的常见等价关系必须记住。

You add and subtract fractions with the same denominator, and with different denominators by finding a common denominator. Multiplication and division of fractions are introduced: multiply straight across, and divide by multiplying by the reciprocal.

你要进行同分母分数的加减，以及通过寻找公分母进行异分母分数的加减。引入分数的乘除法：直接相乘，除法则是乘以倒数。

Working with mixed numbers and improper fractions is also covered. For example, 2⅓ as an improper fraction is 7/3.

还涉及带分数与假分数。例如，2⅓作为假分数就是7/3。

Percentages are used to find percentages of quantities (e.g., 30% of 200 = 0.3 × 200 = 60) and to express one quantity as a percentage of another.

百分比用于求数量的百分比（例如，200的30% = 0.3 × 200 = 60），以及将一个数量表示为另一个数量的百分比。

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6. Negative Numbers | 负数

Negative numbers represent values below zero. You learn to order, add, subtract, multiply and divide them. The number line helps visualise operations: adding a negative number moves left; subtracting a negative moves right.

负数表示低于零的值。你要学会排序、加减乘除负数。数轴有助于形象化运算：加负数向左移动；减负数向右移动。

Key rules: If signs are the same, the result is positive; if signs are different, the result is negative. For multiplication/division: (-3) × (-4) = 12, and 12 ÷ (-3) = -4.

关键规则：同号得正，异号得负。对于乘除：（-3）×（-4）= 12，而12 ÷（-3）= -4。

You interpret negative numbers in context, such as temperature below freezing, bank overdrafts, or elevations below sea level.

你要在情境中解读负数，例如冰点以下的温度、银行透支或海平面以下的高度。

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7. Algebraic Expressions | 代数表达式

Algebra uses letters (variables) to represent unknown numbers. In Year 7, you simplify expressions by collecting like terms. For example, 2a + 3a = 5a, and 4b – b = 3b. You also multiply variables: 2 × y is written as 2y.

代数用字母（变量）表示未知数。在七年级，你通过合并同类项来化简表达式。例如，2a + 3a = 5a，4b – b = 3b。你还乘变量：2 × y 写作 2y。

You use substitution involving positive and negative integers. If x = 3, then 2x + 5 = 2(3) + 5 = 11.

你进行涉及正负整数的代入。如果 x = 3，那么 2x + 5 = 2(3) + 5 = 11。

Expanding brackets using the distributive law is introduced: 3(x + 4) = 3x + 12.

引入使用分配律展开括号：3(x + 4) = 3x + 12。

You also write expressions from word problems, turning phrases like ‘five more than a number’ into x + 5.

你还要根据文字题写出表达式，将短语 “比一个数多5” 转换为 x + 5。

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8. Solving Linear Equations | 解一元线性方程

Solving an equation means finding the value of the variable that makes it true. Simple one-step equations include: x + 3 = 7 (subtract 3 from both sides → x = 4); 2x = 10 (divide both sides by 2 → x = 5).

解方程就是找出使方程成立的变量的值。简单的一步方程包括：x + 3 = 7（两边同时减3 → x = 4）；2x = 10（两边除以2 → x = 5）。

Two-step equations involve undoing two operations. For 2x + 1 = 9, first subtract 1 from both sides (2x = 8), then divide by 2 (x = 4).

两步方程需要逆运算两步。对于 2x + 1 = 9，先两边减1（2x = 8），再除以2（x = 4）。

You check your solution by substituting it back into the original equation. Always write the solution clearly, e.g., x = 4.

通过将解代回原方程来检验。始终清晰地写出解，例如 x = 4。

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9. Sequences and Patterns | 数列与规律

You recognise and generate sequences based on a term-to-term rule. An arithmetic sequence (linear) adds or subtracts the same difference each time, e.g., 5, 8, 11, 14… (add 3). The n^th term of such a sequence can be found: for 5, 8, 11, 14, the n^th term is 3n + 2.

你要认识并根据项与项之间的规则生成数列。算术数列（线性）每次加上或减去相同的差，例如：5, 8, 11, 14……（加3）。这类数列的第n项可以求出：对于5, 8, 11, 14，第n项是 3n + 2。

You explore other patterns, including square numbers (1, 4, 9, 16…), triangular numbers, and Fibonacci-like sequences.

你还要探索其他规律，包括平方数（1, 4, 9, 16……）、三角形数以及类斐波那契数列。

Using a table of values to describe a pattern is a common skill, linking algebra and geometry.

使用数值表来描述规律是一项常见技能，将代数与几何联系起来。

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10. Angles and Lines | 角与线

You measure and draw angles using a protractor, learning to classify them: acute (less than 90°), right angle (90°), obtuse (between 90° and 180°), straight line (180°), and reflex (more than 180°).

你用量角器测量和绘制角，学会分类：锐角（小于90°）、直角（90°）、钝角（90°到180°之间）、平角（180°）和优角（大于180°）。

Angles on a straight line sum to 180°, and angles around a point sum to 360°. Vertically opposite angles are equal.

直线上的角之和为180°，围绕一点的角之和为360°。对顶角相等。

You also define parallel and perpendicular lines, and calculate missing angles using these facts

Published by TutorHao | Year 7 Mathematics Revision Series | aleveler.com

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